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Many objects of common use (tools, utensils, metals, knick-knacks, dishes and glasses) and artifacts (for example paintings of all types) are composed of two or more layers. In many cases, it would be useful to determine the correct location, composition and thickness of the various layers. Non-destructive and non-invasive methods are described, based on energy-dispersive X-ray fluorescence which are able to 'reconstruct' the complete structure of a multilayered sample. These methods use, in different ways, the ratios of characteristic X-rays emitted by the elements of the layers, and, in particular, two effects can be usefully employed, effects which are based on the differential attenuation of Kα and Kβ or Lα and Lβ X-rays: Different self-attenuation of K or L X-rays emitted by an element characterizing a layer because of the different energy of the two K or L X-rays;, Different attenuation of the two K or L X-rays of an element characterizing a layer by a second superimposed layer., Furthermore, the ratio of the Kα (or Lα) X-rays emitted by an element characterizing the internal layer, to the Kα (or Lα) X-rays emitted by an element characterizing a second superimposed layer, can also be employed in the 'reconstruction' of the layers. In this paper, the theoretical background of all these methods is described, and typical examples are shown. Copyright © 2015 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]